Careful, [itex]\mathbf{i}+2\mathbf{j}[/itex] and [itex]\mathbf{i}[/itex] are not parallel, but their dot product is 1. Likewise, [itex]\mathbf{i}+\mathbf{j}[/itex] and [itex]2\mathbf{i}+2\mathbf{j}[/itex] are parallel but their dot product is not equal to 1.

If 2 vector fields are parallel, what can you say about the angle between them at every point? What does the dot product formula then tell you?

of course! Okay, so the angle is zero or 180. So upon finding the dot product how would I determine the angle between these two fields from the result of this dot product? (2 Sin(θ))/r + (Cos(θ) Sin(2 θ))/r

So upon finding the dot product how would I determine the angle between these two fields from the result of this dot product? (2 Sin(θ))/r + (Cos(θ) Sin(2 θ))/r

Do I just plug in zero for theta?

No, the θ in the equations for your 2 vector fields is either the polar angle (the angle between the position vector and the polar axis) in spherical coordinates, or the azimuthal angle (the angle between the projection of the position vector onto the xy-plane, and the x-axis), depending on which naming convention you are using for spherical coordinates.

That θ is, in general, not the same as the angle between the two vector fields.

If the angle between the two vector fields is 0, then the (correct) dot product equation tells you [itex]\mathbf{A} \cdot \mathbf{B} = |\mathbf{A}||\mathbf{B}|\cos(0)[/itex]